From what I have seen so far, there is a lot of linear algebra. Curious what other kinds of maths are used in QC & the specific fields in which they are most predominately invoked.
closed as too broad by Nelimee, Sanchayan Dutta, heather♦ Jul 16 '18 at 18:17
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- Calculus (e.g. $\int |\psi(x)|^2dx = 1$ )
- Differential Equations (e.g. Schroedinger equation)
- Complex analysis
- Statistics/Probability theory
- Stochastics (especially in studying open quantum systems)
- Information theory
- Topology (e.g. topological quantum computing)
- Group theory (e.g. in stabilizer codes)
- Representation theory (e.g. in stabilizer codes)
- Graph theory (e.g. graph state quantum computing)
- Functional analysis (e.g. Quantum states are unit vectors... with respect to which norm?)
- Algebraic geometry (e.g. for factoring numbers using quantum annealing)
- Discrete optimization (e.g. for factoring numbers using quantum annealing and also.)
- Optimal control theory (here's a review on quantum optimal control theory)
- Game theory (for quantum games)
- Boolean algebra (see this book on Boolean functions and quantum mechanics)
- Coding theory (e.g. Quantum Error Correcting codes)
- Number theory (e.g. Shor's algorithm)
- Category theory (e.g. What is the use of Categorical quantum mechanics?)
- Differential geometry (for quantum information theorists working on quantum gravity)
- Formal Language Theory (in studying QC as a computation model)
- Amazingly, I've even seen fractional calculus come up for sub-Ohmic baths (s=1/2 in this)
- Basically any area of mathematics because we would like to make quantum algorithms to do things more efficiently, regardless of the mathematical field. For example "semi-definite programming" could be added to the list, because quantum algorithms for semi-definite programming is a very active current area of research.
- A better question might be "is there any area of mathematics for which you cannot see any possible connection to quantum computing?"